1. Field of the Invention
The present invention relates to a recording medium and a determination method.
2. Description of the Related Art
Along with the recent miniaturization of semiconductor devices, it has become difficult for an exposure apparatus to transfer (resolve) patterns corresponding to such microdevices. Under the circumstance, to keep up with miniaturization of semiconductor devices, an exposure apparatus employs resolution enhanced technologies such as modified illumination and OPC (Optical Proximity Correction) and technology optimizing the pattern of a mask and the illumination shape (effective light source distribution) with which the mask is illuminated. The illumination shape (effective light source distribution) is a light intensity distribution formed on the pupil plane of an illumination optical system and is also the angular distribution of light which illuminates a mask.
To optimize the illumination shape, the device layout pattern (target pattern), the evaluation positions in a transfer pattern (optical image), and the evaluation values (e.g., the dimensions, the DOF, and the exposure margin) at the evaluation positions are set first. Next, a transfer pattern is calculated while changing the illumination shape, and the evaluation values at the evaluation positions in the transfer pattern are obtained. The transfer pattern calculation and the evaluation value obtaining are repeated until the evaluation values satisfy evaluation references (evaluation criterions) or the number of times of change in illumination shape reaches a predetermined number. The illumination shape is expressed numerically. For example, annular illumination having a constant intensity is expressed by a function having inner σ and outer σ as parameters (variables), and these parameters are optimized using, for example, a Monte Carlo method. Note that the same pattern naturally yields different transfer patterns when different illumination shapes are used, so the transfer pattern shifts from the target pattern upon changing the illumination shape. For this reason, OPC for matching the transfer pattern with the target pattern is necessary in that case. OPC is performed every time the illumination shape is changed or when the illumination shape is changed by a predetermined amount.
Also, U.S. Pat. No. 6,563,566 (to be referred to as “patent reference 1” hereinafter) proposes a technique of setting a pattern to be formed on a substrate (wafer) and calculating a mathematically optimized mask pattern and illumination shape. The technique in patent reference 1 analytically calculates the solutions (the mask pattern and illumination shape) instead of repetitive computation. Although the technique in patent reference 1 does not adopt OPC, it is an illumination shape optimization technique including mask pattern correction in a broad sense because it copes with a situation in which a pattern to be formed on a substrate (for example, a wafer) is different from an optimized mask pattern. The technique in patent reference 1 has a merit of analytically calculating the solutions, but requires limiting the evaluation value to the tilt of an optical image and, additionally, limiting the number of types of patterns to be formed on a substrate to one. In this manner, the technique in patent reference 1 is impracticable because it has a demerit that there exist small degrees of freedom.
Moreover, Japanese Patent Laid-Open No. 2004-079714 proposes a technique of optimizing the mask pattern and illumination shape in this way.
Unfortunately, the conventional techniques that relate to optimization of the mask pattern and illumination shape cannot form patterns, which are rapidly becoming finer, with a sufficiently high accuracy. This is because the conventional techniques separately optimize the mask pattern and illumination shape (i.e., do not optimize them at once). As described above, factors associated with OPC depend on the illumination shape, so it is generally performed after determining (optimizing) the illumination shape. However, it is often the case that the mask pattern deforms upon OPC and so the illumination shape determined before the OPC becomes no longer optimum after the OPC.